1202.2796 (Georg Rohringer et al.)

Local Electronic Correlation at the Two-Particle Level    [PDF]

Georg Rohringer, Angelo Valli, Alessandro Toschi

Electronic correlated systems are often well described by dynamical mean
field theory (DMFT). While DMFT is an exact self-consistent theory in the limit
of infinite coordination number or dimensions, when applying it as an
approximation to finite-dimensional systems, its self-consistency is guaranteed
at the one-particle level only, i.e., for the local Green function and
self-energy. However, extremely valuable information is also enclosed in the
local two-particle Green functions and vertices. In fact, even at the DMFT
level, mastering the calculation of two-particle quantities is crucial to
compute momentum-dependent response functions that can be compared directly
with experiments. Moreover, the knowledge of the local two-particle Green
function represents the main ingredient for including non-local spatial
correlations at all length scales by means of diagrammatic extensions of DMFT,
such as the dynamical vertex approximation (D$\Gamma$A) or the dual fermion
approach. As hitherto the investigation of local two-particle properties has
been merely sporadic, we present here a systematic analysis of the local
reducible and irreducible two-particle vertex functions for the Hubbard model
at the DMFT level in the context of an unified diagrammatic formalism,
providing an interpretation of the observed frequency structures in terms of
perturbation theory results and of the mapping onto the attractive Hubbard
model.

View original: http://arxiv.org/abs/1202.2796